Christmas time visit to barcelona + suggestion to other nearby places

Saying hello from India. I am going to visit Barcelona (because of the warmer weather) during Christmas break for 11 days with two kids (aged 2 and 5). I have been told that 4-5 days would be a good time to look around the spots in Barcelona.

So I am looking for suggestions to travel around which have warmer climate like Barcelona. It seems Madrid would be much cooler so that might be a problem. I would prefer to travel around in Train to go to other town/cities if possible.

Also, what things should I keep in mind during the Christmas Eve/Day? I suppose most of the things would be closed.

Amsterdam hotels, what's the best place to stay in Amsterdam ?

My wife and I are planning to visit Amsterdam at the end of November, to celebrate our 10th wedding anniversary. We are mainly interested in museums ( Rijksmuseum, Van Gogh Museum, Anne Frank House and Rembrandt House Museum ) and the channels.

We are not really sure about where to book the hotel, what is the best neighborhood to stay in Amsterdam ? Any recommendations for not overly expensive hotels in Amsterdam ? We want to reach everything by foot, if possible.